Transient dynamics and their control in time-delay autonomous Boolean ring networks.

Biochemical systems with switch-like interactions, such as gene regulatory networks, are well modeled by autonomous Boolean networks. Specifically, the topology and logic of gene interactions can be described by systems of continuous piecewise-linear differential equations, enabling analytical predictions of the dynamics of specific networks. However, most models do not account for time delays along links associated with spatial transport, mRNA transcription, and translation.

Super-transient scaling in time-delay autonomous Boolean network motifs.

Autonomous Boolean networks are commonly used to model the dynamics of gene regulatory networks and allow for the prediction of stable dynamical attractors. However, most models do not account for time delays along the network links and noise, which are crucial features of real biological systems. Concentrating on two paradigmatic motifs, the toggle switch and the repressilator, we develop an experimental testbed that explicitly includes both inter-node time delays and noise using digital logic elements on field-programmable gate arrays.

Reservoir computing with a single time-delay autonomous Boolean node.

We demonstrate reservoir computing with a physical system using a single autonomous Boolean logic element with time-delay feedback. The system generates a chaotic transient with a window of consistency lasting between 30 and 300 ns, which we show is sufficient for reservoir computing. We then characterize the dependence of computational performance on system parameters to find the best operating point of the reservoir.

Transient scaling and resurgence of chimera states in networks of Boolean phase oscillators.

We study networks of nonlocally coupled electronic oscillators that can be described approximately by a Kuramoto-like model. The experimental networks show long complex transients from random initial conditions on the route to network synchronization. The transients display complex behaviors, including resurgence of chimera states, which are network dynamics where order and disorder coexists.

Temperature-dependent Sellmeier equations for rare-earth sesquioxides.

High-power lasers are making increasing demands on laser hosts especially in the area of thermal management. Traditional hosts, such as YAG, are unsuitable for many high-power applications and therefore, new hosts are being developed including rare-earth sesquioxides. We report new measurements of the refractive indices of these materials as functions of wavelength and temperature, which will aid in the design of laser cavities and other nonlinear optical elements.